The present disclosure relates to a simulation method for predicting a processing state of a processing target, to a simulation program, and to a processing unit and a simulator that utilize the simulation method.
As a predicting technique for semiconductor processing, there is processing shape (etching or deposition) simulation. Two models are known as broad categories of this simulation, that is, a string model and a voxel model. The string model is a model based on a flux method. In the string model, a plurality of lattice points are arranged on a surface of a shape, and a surface reaction is solved numerically at each of the lattice points to derive a reaction rate (an etching rate or a deposition rate). Further, a coordinate of the lattice point is moved in a direction of a normal by an amount of the reaction rate, and the lattice points are connected by a string. The string model is a model that expresses processing shape development in such a manner. The normal to the surface that is necessary upon the processing shape development is derived from position information of the adjacent lattice points. Therefore, a deriving method thereof is simple, but on the other hand, followability with respect to steep variation in shape is not favorable due to the features of the deriving method (strings cross one another).
On the other hand, in the voxel model, a shape is expressed by determining whether or not the arranged voxels exist. Therefore, reproducibility of a complicated shape such as a micro-trench is better than that in the string model. Generally, since the voxel model is a calculation technique that uses Monte Carlo method, it is easy to simulate gas transport such as ion and radical transport in a pattern, and micro physical phenomenon and chemical reaction on the surface. However, there are some fundamental issues since the voxel model is a calculation technique that uses the Monte Carlo method. For example, there may be the following issues in the voxel model: calculation load is large; calculation precision and calculation load are in a relationship of trade-off; and a method of deriving a normal with the use of the position information of a voxel from a region having asperities on the surface is difficult since the shape is expressed with the use of voxels.
As an improved version of these calculation techniques, a voxel model based on the flux method (TIGER: Topography Image GEneration Routine) has been proposed (see Japanese patents No. 3188926 and No. 2687270 and “IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems. Vol. 16, No. 4, 1997”). This calculation technique calculates gas transport and surface reaction based on the flux method and is an approximate technique that does not derive a normal to the processed surface. Therefore, this technique calculates faster than the voxel model based on the Monte Carlo method. Further, a reaction rate (an etching rate or a deposition rate) is calculated from a simple surface reaction called a unified model with the use of a gas flux that perpendicularly enters each face of voxels, and thereby, the shape is expressed. At this time, an oval sphere defined by the reaction rate is given, and the voxels in the oval sphere region are removed (etched) or added (deposited). Therefore, this technique achieves more stable shape reproduction that has a smoother surface compared to the simple voxel model.